Abstract
This paper is concerned with a numerical method for the time-fractional Benjamin–Bona–Mahony (BBM) equation whose solution typically exhibits a weak singularity at the initial time. Lyu and Vong (2019) presented a linearized difference method of second-order in space and third-order in time. We improve their result by proposing a linearized and compact difference method which is fourth-order in space while keeping third-order in time. By using discrete energy analysis, the unconditional convergence of the proposed method is rigorously proved and the optimal H1-norm error estimate is obtained. Numerical results confirm the theoretical convergence result.
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